Coulomb's Law Electric Fields

1. The problem statement, all variables and given/known data
Two point charges are placed at the opposite corners of a rectangle as shown. What is the Electrical Field magnitude at each point due to the charges?

2. Relevant equations

Pythagorean theorem, E=kq/r^2

3. The attempt at a solution

r= square root of .8^2 +.4^2 =.89
E= 8.99x10^9 X 4X10^-6 divided by (.89^2)
E=8.99x10^9 X 2X 10^-6 divided by (.89^2)
should I not be dividing by .89^2 but rather the radius of an electron?

I am not sure if A and B should be negative or positive or if I am doing this right..?

A and B are points, they are neither negative nor positive.
However, you do need to bear in mind that the electric field is a vector - you only have the equation for the magnitude.

Note, charge 1 is twice the size of charge 2.
For each point, one charge is twice the distance that the other charge is.
It's worth thinking about this - if you double r, then E goes down by... but what if you also double q? ... halve q?

Note: the i direction is usually to the right horizontally - the direction of the field at A due to the 4mcC charge is to the left ... i.e. the -i direction. But it makes no difference to the magnitude.

I don't check people's arithmetic - but your method is now correct.
Can you see where your thinking was out before?

It is a very common tactic to get you familiar with how the equations work by giving you problems where things get doubled and halved. This is a case in point.

Note, charge 1 is twice the size of charge 2.
For each point, one charge is twice the distance that the other charge is.
It's worth thinking about this - if you double r, then E goes down by... (how much?) but what if you also double q? ... halve q?

The point of the exercise is to understand the inverse-square law, not just be able to do the math.